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<title>Geometry in PTC</title>
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<p>The geometrical information is in type
<a href="../../a_def_frame_patch_chart.htm#CHART" style="text-decoration: none; font-weight: 700">
CHART</a>. In PTC, the chart contains a <b><font color="#ff00ff">
<a href="../../a_def_frame_patch_chart.htm#MAGNET_FRAME" style="text-decoration: none">
MAGNET_FRAME</a></font></b><a href="../../a_def_frame_patch_chart.htm#MAGNET_FRAME" style="text-decoration: none">.
<font color="#000000">The magnet frame locates the front, the centre and the
</font></a>end of the fibre. </p>
<p>The reader geometry of a planar fibre is shown below: please click on picture 
to magnify.</p>
<p><a href="planar.jpg">
<img border="0" src="planar.jpg" width="500" height="429" align="left"></a></p>
<p>&nbsp;</p>
<p>Looking at this picture we see that PTC has amount of redundant information 
about standard planar magnets.</p>
<p>The fibre desired location is specified by the position FIBRE%CHART%F%A(3) 
and by the vector triad basis FIBRE%CHART%F%ENT(3,3). The other two sets of 
affine bases are redundant and can be deduced from the magnet geometry.</p>
<p>One notices that the actual magnet is displaced (misalignments) from its 
desired position and that a totally independent set of affine bases are located 
on the magnet. In the absence of misalignments they merge with the fibre bases. </p>
<p>We showed here a typical planar magnet. Things are more complex with the 
vertical bends which follow the MAD8 convention. We delay this discussion. </p>
<p>Now some operators acting on the affine bases:</p>
<p>&nbsp;</p>
<p>&nbsp;</p>
<p>We now describe the purely geometrical operations of PTC on affine bases of 
the type (A(3),ENT(3,3)) . These operations are crucial in order to compute 
patches and misalignments.</p>
<ol>
  <li><a href="geo1.htm">Rotating frames in the PTC order</a></li>
  <li>&nbsp;</li>
</ol>
<p>&nbsp;</p>

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